The thermal voltage rise in supercapacitors can be used to convert efficiently low-grade heat into electric energy.

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kBT /σ 2 with a small anisotropy of about 0.025 kBT and stiffnesses with e.g. 0.53 kBT /σ 2 for the (001) orientation and 1.03 kBT /σ 2 for the (111) orientation. Here kBT is denoting the thermal energy and σ the hard sphere diameter. We compare our results with existing experimental findings.PACS numbers: 68.08. De, 05.20.Jj, 82.70.Dd Solidification and melting processes involve crystal-fluid interfaces that separate the disordered from the ordered phase. Understanding the properties of such interfaces on a microscopic scale is pivotal to control and optimize crystal nucleation and the emerging microstructure of the material. Important applications include the fabrication of defect-free metallic alloys [1] and of photonic [2], phononic [3] and protein [4] crystals. In equilibrium, i.e. between a coexisting crystal and fluid phase, creating a crystal-fluid interface results in a free energy penalty per area that is called interfacial tension. Unlike the liquid-gas or fluid-fluid interface, the structure of the solid-fluid interface depends on its orientation [5]. This anisotropy is associated with a difference between the interfacial tension and the interfacial stiffness of a crystalline surface.Predicting crystal-fluid interfacial tensions by a molecular theory is a very challenging task. Classical density functional theory of freezing provides a unifying framework to describe the solid and liquid on the same footing and is therefore in principle a promising tool. In this respect, the simple athermal hard sphere system which exhibits a freezing transition from a fluid into a face-centered-cubic (fcc) crystal, is an important reference system. The accuracy of previous density functional calculations of the hard sphere solid-fluid interface [6-9], however, was hampered by the lack of knowledge of a reliable functional and severe restrictions in the parametrization of the trial density profile.In this letter, interfacial tensions and stiffnesses of the equilibrium hard sphere crystal-fluid interface are predicted using fundamental measure density functional theory [10] which has been shown to predict accurate bulk freezing data [11]. The interfacial tension and stiffness for five different orientations are obtained, namely along the (001), (011), (111), (012) and (112) orientations (see Fig. 1). A small orientational anisotropy for the tensions is found and the average tension is about 0.66 k B T /σ 2 with k B T denoting the thermal energy and σ the hard sphere diameter. For the stiffnesses the data are spread in a much wider range between 0.28 k B T /σ 2 for the (011) orientation with lateral direction [100] and 1.03 k B T /σ 2 for the (111) orientation. We have als...

We perform a comparative study of the free energies and the density distributions in hard-sphere crystals using Monte Carlo simulations and density functional theory ͑employing Fundamental Measure functionals͒. Using a recently introduced technique ͓T. Schilling and F. Schmid, J. Chem. Phys. 131, 231102 ͑2009͔͒ we obtain crystal free energies to a high precision. The free energies from fundamental measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between fundamental measure theory and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that fundamental measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of fundamental measure functionals studied, only the White Bear II functional ͓H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter 18, 8413 ͑2006͔͒ exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.

Capacitive mixing (CAPMIX) and capacitive deionization (CDI) are promising candidates for harvesting clean, renewable energy and for the energy efficient production of potable water, respectively. Both CAPMIX and CDI involve water-immersed porous carbon (supercapacitors) electrodes at voltages of the order of hundreds of millivolts, such that counter-ionic packing is important for the electric double layer (EDL) which forms near the surfaces of these porous materials. Thus, we propose a density functional theory (DFT) to model the EDL, where the White-Bear mark II fundamental measure theory functional is combined with a mean-field Coulombic and a mean spherical approximation-type correction to describe the interplay between dense packing and electrostatics, in good agreement with molecular dynamics simulations. We discuss the concentration-dependent potential rise due to changes in the chemical potential in capacitors in the context of an over-ideal theoretical description and its impact on energy harvesting and water desalination. Compared to less elaborate mean-field models our DFT calculations reveal a higher work output for blue-energy cycles and a higher energy demand for desalination cycles.

Inspired by recent experimental observations of anomalously large decay lengths in concentrated electrolytes, we revisit the Restricted Primitive Model (RPM) for an aqueous electrolyte. We investigate the asymptotic decay lengths of the one-body ionic density profiles for the RPM in contact with a planar electrode using classical Density Functional Theory (DFT) and compare these with the decay lengths of the corresponding two-body correlation functions in bulk systems, obtained in previous Integral Equation Theory (IET) studies. Extensive Molecular Dynamics (MD) simulations are employed to complement the DFT and IET predictions. Our DFT calculations incorporate electrostatic interactions between the ions using three different (existing) approaches: one is based on the simplest mean-field treatment of Coulomb interactions (MFC), while the other two employ the Mean Spherical Approximation (MSA). The MSAc invokes only the MSA bulk direct correlation function, whereas the MSAu also incorporates the MSA bulk internal energy. Although MSAu yields profiles that are in excellent agreement with MD simulations in the near field, in the far field, we observe that the decay lengths are consistent between IET, MSAc, and MD simulations, whereas those from MFC and MSAu deviate significantly. Using DFT, we calculated the solvation force, which relates directly to surface force experiments. We find that its decay length is neither qualitatively nor quantitatively close to the large decay lengths measured in experiments and conclude that the latter cannot be accounted for by the primitive model. The anomalously large decay lengths found in surface force measurements require an explanation that lies beyond primitive models.

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We show that sustainably harvesting "blue" energy from the spontaneous mixing process of fresh and salty water can be boosted by varying the water temperature during a capacitive mixing process. Our modified Poisson-Boltzmann calculations predict a strong temperature dependence of the electrostatic potential of a charged electrode in contact with an adjacent aqueous 1∶1 electrolyte. We propose to exploit this dependence to boost the efficiency of capacitive blue engines, which are based on cyclically charging and discharging nanoporous supercapacitors immersed in salty and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. We show that the energy output of blue engines can be increased by a factor of order 2 if warm (waste-heated) fresh water is mixed with cold sea water. Moreover, the underlying physics can also be used to optimize the reverse process of capacitive desalination of water. DOI: 10.1103/PhysRevLett.113.268501 PACS numbers: 92.05.Jn, 82.47.Uv, 84.60.Rb, 92.40.Qk In river mouths an enormous free-energy dissipation of the order of 2 kJ takes place for every liter of fresh river water that mixes with an excess of salty sea water. This so-called "blue energy" can nowadays be harvested due to newly available nanostructured materials such as selective membranes [1,2] and nanoporous electrodes [3,4], as also used in supercapacitors [5]. In fact, several test factories have been built based either on pressure-retarded osmosis using waterpermeable membranes [6,7] or on reverse-electrode dialysis using ion-selective membranes [8], and recently a lot of progress has been made with capacitive mixing processes that involve highly porous carbide derived electrodes [9][10][11]. In all these cases, the spontaneous and irreversible ionic mixing process is intercepted and converted to a voltage difference by an enginelike device, very much in the spirit of a Stirling or Carnot engine that intercepts the spontaneous heat flow between a hot and a cold heat bath and converts it (partially) to the mechanical energy of a rotating flywheel [12]. However, the temperature of the river and sea water has been assumed constant throughout the cycle in all devices considered so far. Given the intrinsic scientific and societal interest in combined chemical-heat engines and heat-to-power converters, the ongoing development and upscaling of blue-energy devices and test factories, and the availability of a lot of waste heat in the form of "warmish" water in the industrial world, it is timely to consider temperature tuning in blue-energy devices. In this Letter we predict that the work extracted from capacitive mixing devices can be boosted by a factor of order 2 if warm fresh water is mixed with cold salty water. Moreover, we show how varying the temperature during a desalination cycle reduces the required energy input substantially, and we predict on the basis of a general thermodynamic argument that adiabatic (dis)charging processes lead to significant temperature changes on the order of several deg...